Cylindrical boxes of Oats probably wastes a few cents a box, considering that warehouse, truck cargo and shelf space costs money, and the cylindrical box is an inefficient user of space. Plus, probably a higher cost of the packaging itself at the processing plant, since pallets of cylindrical boxes are harder to prepare for packing than rectangular ones..

You ask this as the number of round-box offerings plunges. Even Quaker is using other container types for most sizes these days.

Round containers can be made leak-proof (dust and grit) more easily than folded boxes, eliminating the need for an inner liner. Oatmeal doesn't degrade the way most cereals do with slight exposure to air and humidity, so it doesn't need to be sealed the way crisper cereals and grains are. So: round boxes were a better choice, back when. I seem to recall them being used for a variety of such products, all powdery and prone to grit and dust leakage but not needing air-sealing.

I buy my oats (steel-cut FTW!) in bulk and store them in a 3-quart cylindrical plastic container, mainly because I can dip into it with a measuring cup. Maybe that's part of the reason. Or distinctive packaging is a marketing strategy.

while they are stronger as an above ground silo, one of the major reasons was freshness. silage could sit in corners and rot, wasting that material and contaminating/inoculating new material. circular could be emptied out better.

Oatmeal is sold in cylindrical boxes? I don't think I've ever seen that here.

Possibly it's sold that way in some areas because people have come to expect a certain packaging? Like the way teflon tape for plumbing is sold in those odd little plastic spools: people expect it to be packaged that way, and will miss ones that aren't.

Why are you talking about packaging efficiency with respect to cereal boxes? Cereals have a long tradition of using a lot more packaging than needed simply so they look like they contain more product than they actually do.

One advantage to the round top is that it's easier to scoop the oatmeal out. I can easily dip my measuring cup in to get exactly what I need. I buy steel-cut oats in a box and pour them into an old Quaker Oats cylinder for this reason.

When you try to ship a case of them. A dozen boxes can be placed in a shipping carton with no wasted space but a dozen cylinders of Quaker Oats leaves wasted space. You may notice that many juice drinks are now sold in plastic jugs that are squarer than previously. (See this photo of Naked Juice bottles as an example.)

Packing factor. Rectangular boxes can be pressed up against each other with no appreciable gaps between the edges. No wasted space. Round cylinders have dead space in the interstices between the round bits.

Here is the 3-D version using spheres. 2-D has similar packing factor.

Imagine a square grid of circles, aligned in columns and rows. If all the circles are in straight columns and rows, you get lots of gap between the curves.

Code:

OOOOOO
OOOOOO
OOOOOO

Now look at the "honeycomb" pattern, where the second row is offset by half a diameter, so it fits into the gap between the two above it in the first row. (I can't indent a half-space, but I think this suggests the idea.)

Code:

OOOOOO
OOOOOO
OOOOOO

Tighter packing factor, still some dead space.

Here is a discussion of circle packing. Scroll down to the pretty pictures. See the one labeled "Square"? That is the first example above. Look at the yellow compared to black. Now look at the one labeled "Triangular". Notice how there is less yellow, less wasted space. That is the physical demonstration of packing factor, i.e. measure of wasted space.

Rectangles of consistent size are much more efficient than round things.

Why are you talking about packaging efficiency with respect to cereal boxes? Cereals have a long tradition of using a lot more packaging than needed simply so they look like they contain more product than they actually do.

Cereal boxes often come with the disclaimer "some settling may have occurred during transportation" or the like. This is because the packaging has to take into consideration the volume of a loose packing of the cereal within the box and the settling that occurs during handling.

All of those little cereal bits are knobby, bumpy, odd-shaped bits of various sizes. When being handled at the factory and placed into packaging, the are typically poured from a hopper or whatnot into the top of the package. This means all those odd bits come together in random arrangements, which makes for a loose packing factor. There is a reasonably consistent range of volume that will fill for a certain weight of product. The packaging has to accommodate this loosest packing factor fit to sell by weight.

During handling, i.e. transportation from along the assembly line, into trucks, transported to stores, loaded on shelfs, into carts, past the checker, through your car, to your shelf, and eventually your table, there is a lot of shaking going on. Shaking has the effect of sorting the bits to more efficient packing shapes. In other words, loose bits move around, smaller pieces settle through larger ones, shapes wiggle and shift and move into empty spaces created during the loose fill process.

When you open the box, excess volume air has moved to the top of the box as all the pieces of cereal are more tightly packed in the box. That is settling, which makes it look like they shipped you a half-empty box. They did, but that gap was spread around in the box when they filled it. You bought the weight of product they told you you were getting. And some air from handling.

Plus, open the lid, if the package is not sufficiently rigid, there may be bowing of the box sides, letting the product settle a bit lower.

Incidentally, chips often come with extra air nitrogen in their bags on purpose - that space and nitrogen serves to cushion the chips so they to not get as squashed during handling. The internal pressure keeps the bag inflated like a balloon, rather than getting flattened.

I've seen jam jars that are octagonal. No way to avoid wasted space with those (you're left with small open squares in the middle and open triangles around the edge), but they do fill space a bit more efficiently than round jars.

When oats are harvested, they are in hulled shells and are round. Processing begins by removing the hulls, and separating the oats and oat pieces by size. Some of the oat groats (i.e. unprocessed oat seeds) are broken during the handling.

Later, whole oats can be cut to make more of the smaller oat pieces. Any oat pieces of varying sizes, whether deliberately cut or broken during the handling process, are called "steel cut".

The whole oats and sized oat pieces are then processed by either rolling to make flakes (rolled oats), or ground to make flour (after separating the bran). Apparently the different sizes and thickness of oat flakes are marketed and used separately.